Lewis & Short

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irrătĭōnābĭlis (inr-), e, adj., without reason, irrational (post-class.; not in Quint., v. Spald. ad Quint. 2, 16, 16): error, App. Dogm. Plat. p. 21: motus, Amm. 31, 12, 15.
Of musical intervals, = logica, proportional, harmonic: irrationabilia (sunt) quibus non subest ratio, Mart. Cap. 9, § 949.
Subst.: irrătĭōnābĭlĭa, ĭum, n., unreasoning creatures, Lact. 2, 2, 17.
Adv.: irrătĭōnābĭlĭter, irrationally, Amm. 19, 10, 1; Tert. Poen. 2; Cael. Aur. Acut. 2, 37, 199.

* irrătĭōnābĭlĭtas (inr-), ātis, f. [irrationabilis], irrationality, App. Trism. p. 92, 1.

irrătĭōnābĭlĭter, adv., v. irrationabilis fin.

irrătĭōnālis (inr-), e, adj. [2. in-rationalis], without reason, irrational (postAug.): animal, Quint. 7, 3, 3; 24; Sen. Ep. 113, 17; 118, 14; 124, 23: usus, mechanical exercises, Quint. 10, 7, 11: anima, Tert. Poen. 12.
Subst.: irrătĭōnālĭa, ĭum, n. plur., things or creatures without reason: de irrationalibus, Quint. 8, 6, 13.
Adv.: irră-tĭōnālĭter, irrationally, Tert. adv. Marc. 2, 6 al.